Some machines are already known for plastic film packaging of a plurality of articles such as cans, bottles, boxes and so on, either loose or collected on a tray. By means of said machines either a complete packaging of the articles is performed, i.e. with the plastic film wrapped around all the faces of the group of articles or container thereof, or a so-called bundling, i.e. wrapping the film around the peripheral faces of the group of articles, leaving two opposite faces unwrapped. Particularly for bundling, the known machines use a hot shrinking kind of plastic film, i.e. a type of film that shrinks when subjected to heating whereby the group of articles wrapped by the film get tightly enclosed. In order to obtain said shrinking, the film wrapped group of articles is passed through a heating tunnel which requires a larger floor area and a consumption of energy besides an environment temperature increase in the manufacturing rooms. The user of a heating tunnel causes even more drawbacks when the packaged products are likely to deteriorate if subjected to heat. Therefore, taking said drawbacks into account, attempts have been made to replace heat shrinking films with cold stretchable or partially cold stretchable films, i.e. those plastic material films which, after having been cold stretched exhibit the so-called "elastic memory" bringing them back substantially to the starting dimensions. While cold stretchable films have replaced the heat shrinking ones in the packaging of a large variety of articles,they have not been used yet for bundling operations, wherein heat shrinking films are still the preferred kind. The reason why they are still preferred should be sought in the fact that the machines used up to now for cold stretchable film packaging lack the ability to uniformly stretch the film in the longitudinal direction, that is in such a way as to avoid sideways shrinking. In fact, it is already known that when a film web gets longitudinally stretched, it tends to shrink transverse to the stretching direction, the shrinking effect reaching its maximum in an area half way between the end portions being clamped by the stretching means. Therefore, if a film web having the same width as a container were used for bundling said container, after stretching the container side contacting the central shrunk area of the film would not be completely covered by the same, whereby the bundling would be substantially ineffective. If attempts were made to correct said drawback by increasing the film transverse dimensions in order to compensate for strech dependent transverse shrinking, a problem would still arise at the end portions of the films in that the film would hang out of the corners of the bundled container, whereby bundling uniformity would be lost and film would be unavoidably wasted.